My first experiment with ungrading: Final review

(A portion of) David’s wall-o-games

In Fall 2021, I took my first steps into the world of ungrading. Inspired by Susan D. Blum’s Ungrading, I went fully gradeless in my upper-level Euclidean Geometry class. I gave only feedback on student work, with no grades on any assignment. The general plan was to have students describe how they met criteria for success that I laid out, include a portfolio of their work to support it, and decide for themselves what final course grade that led to.

Let’s look back on my first semester of ungrading and see how things went.

Did my students learn?

Before I get into more details, I should say this: After teaching at least 12 sections of geometry over the years, this was the best semester of geometry I’ve ever taught. Students were energetic, interested, asked great questions, engaged in excellent collaboration. They willingly struggled, failed, reflected, tried again, and did an amazing job of supporting each other.

In that whole last paragraph, notice that I didn’t say anything about grades. That’s not what mattered.

These students were juniors and seniors, so they each had at least one normal semester of college before “the great pivot” in March 2020. They were eager to get back to normal (whatever that means) and I credit that desire with bringing much of the extra energy into our class. I just had to help them on their way.

So, what did I notice about learning? Students learned a lot, and they improved significantly during the semester. This is a class where I try to help students move from a rigid, “there’s only one way to do it and there’s always one correct answer” approach to math into a more nuanced view. They learn about the subtleties of mathematical argument by presenting to each other in class. They learn why high school geometry is the way it is, but they also discover that there isn’t just one correct set of “rules”: Mathematicians can choose the rules of geometry, follow them to their logical ends, and build entirely new worlds through these choices.

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This is a class full of big, challenging ideas.

In most semesters, student move in these directions, but many move only a little, and some I can never get to budge. They want to stick with their existing understanding of geometry and how it works, get that “one right answer” and (this is the part that really terrifies me) teach their future students in the exact same way. This year, nearly everyone made huge strides in their growth and understanding. It was really amazing to see this happen.

And again — none of this had anything to do with grades. The grades got out of the way and let us learn.

But what about grades?

Because this was an ungraded class, the focus was on feedback. Students got lots of questions and suggestions, both from classmates and from me, as they gave in-class presentations and discovered proofs in teams. On homework, I gave students detailed written feedback, phrased in terms of clear “homework objectives”, but no grades. Students could resubmit one revised proof each week and get my feedback on the revision. Many students called out the homework-revision feedback loop as especially helpful in growing and solidifying their understanding.

Each student completed two “check-in reflections”, in weeks 5 and 10 (of 15). In these structured written assignments, students reflected on their progress and made an estimate of their grade. You can find more details of the class setup in my midterm reflection about this ungrading experiment, including the complete portfolio instructions and grade criteria.

I offered optional 20 minute Zoom meetings to talk about their progress. Either the student or I could request a meeting.

I almost always agreed with students’ self-reflections and their self-assigned grades. In the first round of meetings, there were two or three students who (in my opinion) significantly over-estimated their progress, usually because they misunderstood some of the criteria for success in our class. I stepped them through some questions to help them understand why we disagreed, and afterwards we were in much closer agreement.

More commonly, students were harder on themselves than I would have been, giving reasons like “I know I still struggle with this idea, even if my final work looks good” or “I’ve presented a few times, but not a lot”. If there was something to work on, we made a clear plan for how to get there. But when I thought they were already making great progress, I tried to use their concerns to suggest directions to stretch and grow in the coming weeks.

Some students internalized the idea that they had to get things right on the first attempt or else they could never be good enough. A common refrain I heard was “But I have to revise my homework before it’s fully correct” to justify a lower grade. This is undoubtedly an artifact of traditional grading systems: They encourage a one-and-done approach that penalizes taking time to learn. I tried to convince everyone that taking advantage of feedback to improve is not just OK, it’s how learning works, but I’m not sure I succeeded.

In all cases, having narrative criteria for final grades gave students clear directions for improvement. This was one of the big wins of the semester.

At the end of the semester, students completed one last written reflection, this time including a portfolio of work that supported their arguments. Students made good arguments for high grades, and they cited their growth and learning with solid evidence. Many students whose midterm grade check-ins had been in the “B/C” range reached an A at the end. A very small number of students made the choice to prioritize other things at the end of the semester, but they also owned that decision and proposed a lower grade in their final reflections.

In case you’re curious, my final grade distribution was heavy with A’s and A-’s, some B’s, and a few C’s. The very few students who didn’t get the grade they argued for all earned a higher grade instead (in every case, raising by 1/3 step, such as from B to B+). I think this is quite representative both of what students learned, and how they grew, during this semester. I can say with certainty that, based on 15 weeks of observing my students present, write, work, and grow, nobody should have earned a failing grade.

What did students think?

In both the final portfolios and our anonymous end-of-semester surveys, students had very positive things to say about grades — but, well, they talked about exactly that: grades. They clearly saw a grading system where I didn’t want one. They were happy with it, yes, but they still saw it as grades.

Only a few students called out what I hoped to be major benefits of ungrading. For example: “It made it easier to focus on learning vs trying to get a good grade on each assignment.” or “One aspect I have grown in is reflecting and learning from my mistakes. I often thought mistakes meant failure. However, in this class it was a learning point … [this] allowed me to work on learning the content instead of ‘earning the grade’.”

There were some very positive comments, such as “This is my favorite class”, and quite a few expressions of surprise at how much they enjoyed it. There was also recognition at how much they had grown, especially in writing proofs. Then there’s this, perhaps the most honest of all: “I don’t hate it”.

It’s worth remembering that I work in a bit of a magical fairy land. By the time students reach my geometry class, they’re 3rd or 4th year pre-service teachers who have been through many, many other math and math education classes. They’re familiar with alternative grading systems — in fact, they practically expect them. Here’s another students making an interesting observation: “Self grading is fine, and I see why it can be useful, but I feel like it was an added stressor to keep track of my grade in this class, in [another ungraded class], and then a workload of 15 credits. Now, if there is to be a self grading system, this is the way to go.”

Were the grades really gone?

Well… kind of.

In my midterm reflection on ungrading, I said that “it seems like the lack of grades is barely on anyone’s radar”. Students were more focused on geometry, and that’s exactly what I wanted! This changed somewhat in the second half of the semester.

Each homework included specific objectives — ideas to practice using and working with, varying from week to week — and I tried to put feedback in terms of those areas. One of the criteria that students used to decide on their final grades was to “consistently meet the homework objectives (possibly after revision)”.

Many students came to see “meeting objectives” as a kind of grade. If I didn’t clearly state something like “you’ve met all of the objectives on this homework”, they would ask. Another criterion was to write “exemplary” proofs, and again, this provoked many questions: “Is this exemplary yet?”

Homework had much more focus on feedback than in past classes, but students still saw the objectives as a “checkbox” to meet. In other words, students saw a game, and they played it. Students are used to playing games — so much so that they saw a game even where I didn’t want there to be one.

My refrain throughout the semester was “I want you to focus on learning and growing, not on grades.” Some students bought into that, but as the semester went on, I think the pull of the grades became too great in their minds. They knew there would be final grades, and they couldn't avoid thinking about them.

I noticed that grades were creeping into my class, but I didn't find a way to resolve it to my satisfaction. Later in the semester, I started including “magic words” in my feedback, as in “This is an exemplary solution!” So I basically was assigning marks, although with the interesting twist that I didn’t require any specific number of these marks for the final grade.

Interestingly, students said a lot about how helpful the homework feedback was and how much they learned through the revision feedback loop. So while grades may have crept in, there was still an increased emphasis on feedback, and students felt the benefit of it.

The final grade criteria also looked a lot like grades, in a Specifications sort of way: Here’s a list of requirements; complete (most of) them to earn an A. For a B, complete fewer criteria or less thoroughly, and so on. Even though I didn’t require specific numbers of anything, students also looked at this as a checklist, and I can’t really disagree: That’s what it was, intended or not. Despite the fact that grade descriptions made it clear that students didn’t need to meet all of the criteria, most students tried to argue that they met all of them, even students who were arguing for a B or C as their final grade. Again, students saw a game, and so they played it.

Playing the game

To tie things up, I want to introduce an analogy that I’ve been thinking about lately.

I have some hobbies besides being a mathematician and blogger, and one of the biggest is playing board games. There are a huge variety of board games out there, ranging from traditional and familiar (Monopoly, chess) to much more interesting modern designs (Catan, Ticket to Ride, Wingspan). Some modern games are even cooperative, with all players winning or losing together.

I’ve come to realize that there are some key ways grading systems are like board games. Like board games, grading systems have rules and each “player” gets a final score. Instructors create the rules, and students play using them, trying to “win”. Many traditional grading systems have muddy rules that lead to miserable scenarios. Think about the classic Monopoly situation: Your brother manages to build a bunch of hotels, you keep landing on them, and pretty soon you’re bankrupt and can never recover.

We often talk about how alternative systems like Standards-Based Grading and Specifications change the game. But — and this is my point in all of this — SBG and Specifications are still games. They have clearer rules, they’re more fun, and they let players recover from early mistakes. But in the end, they are still games. There’s still a final score, and everyone knows it’s coming. Students play the game with this knowledge in front of them.

I think it’s fair to say that ungraders would like there to be no game (or grades) at all. But given that the vast majority of us live in institutions that mandate we play a game (final grades), ungraders instead try to disrupt the inner workings of the game as much as possible. Some ungraders make up the rules in collaboration with the players. Others ask the players to decide for themselves how well they played at the end of the game. Some try to remove all of the rules and let players run around in a sandbox world.

And this is definitely doable: There are games where I can get so immersed in the fun, that I don’t particularly care what happens at the end. As an undergrad, I was lucky enough to take some classes that were also run this way: The class itself was exciting and interesting, and grades were mostly out of sight. Having experienced this helped me be confident that I could successfully use ungrading in my own classes. Then again, there are games (and classes) where every move is all about optimizing your final score.

I don’t want to sound like I’m trivializing grades nor teaching by comparing them to games. One reason that I enjoy board games is because they involve learning and growth. Within the structure of a game, I can explore new strategies, try new things, solve puzzles, and grow in my understanding. I think that this is a fair goal for grades as well: To provide just enough structure to encourage learning and growth, without getting in the way of it.

In my ungraded Euclidean Geometry, my students could see that there was still a game. But they also understood that I wanted them to go beyond: To learn, to struggle, to fail, and to have the space to grow as they did so. I think that I managed to create a game that gave them room to do this, even if it was imperfect and got in the way some times. I, too, learned a lot about the game we were playing.

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1. This isn’t abstract math-for-the-sake-of-math, either. Geometry done on the surface of a sphere — like, say, the one we all live on — is both extremely practical and significantly different from Euclidean geometry.